Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=g,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11989840, C8×#3938, #11989845, … |
| maximal normal subgroup of | #11989840, C8×#3938, #11989845, … |
| maximal quotient of | #11987257, #11987260, #11987262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2794);